Explicit Solution for a Family of Hermann Riccati Differential Equations
Explicit Solution for a Family of Hermann Riccati Differential Equations
This paper deals with a parametric family of ordinary differential equations originated by an ancient geometric problem posed in 1719 by the Swiss mathematician Jakob Hermann (1678-1733) and partially solved by Jacopo Vincenzo Riccati (1676-1754). We translate Riccati approach, called by himself dimidiata separazione (splitter, or halved, separation), in modern …